I'm not certain the twist rate will stabilize the 60 grain bullet well enough to get decent accuracy in the old Winchester. It was designed for a 40-45 grain bullet, so you may not get tight groups.
Try 3. grs of Unique, with the 60, and don't go over 4. grains, while working up. If the accuracy is no good, try the same load with a 40 grain. This load is about 1450 fps.